74.3k views
2 votes
You ingest 200 mg of medicine and your body removes 15% of it per hour. How long until there is only 40 mg left?

User Big Zak
by
8.2k points

1 Answer

5 votes

Answer:

The time after which only 40 mg of medicine left inside body is 9.8 hours

Explanation:

Given as :

The initial quantity of medicine ingest in body = i=200 mg

The final quantity of medicine in body = f= 40 mg

The rate at which body remove medicine = r = 15%

Let The time taken to remove = t hours

According to question

The final quantity of medicine in body after t hours = The initial quantity of medicine ingest in body ×
(1-(\textrm rate)/(100))^(\textrm time)

I.e f = i ×
(1-(\textrm r)/(100))^(\textrm t)

Or, 40 mg = 200 mg ×
(1-(\textrm 15)/(100))^(\textrm t)

Or,
(40)/(200) =
(1-(\textrm 15)/(100))^(\textrm t)

Or , 0.2 =
((100 - 15)/(100))^(t)

Or,
((85)/(100))^(t) = 0.2

Taking Log both side

So,
Log_(10)
((85)/(100))^(t) =
Log_(10)0.2

Or, t ×
Log_(10)0.85 =
Log_(10)0.2

Or, t (-0.07) = - 0.69

∴ t =
(.69)/(.07)

I.e t = 9.8 hours

So, The time after which only 40 mg left inside body = t = 9.8 hours

Hence,The time after which only 40 mg of medicine left inside body is 9.8 hours .Answer

User KRONWALLED
by
8.5k points